What is the proportion relating the perimeters of two square figures where the first possesses a diagonal 3 times the length of the second?
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Answer: D. 3:1
Explanation
The perimeter of any square is directly proportional to the length of its side. The diagonal of a square is directly proportional to its side length by the square root of two. Since the ratio of their diagonals is three to one, their perimeters share that exact same ratio. Similar geometric figures maintain constant linear ratios across all corresponding dimensions and perimeters. Scaling the diagonal of a square scales its sides and perimeter by the identical factor. Perimeter calculation involves multiplying the side length by the constant integer four.
Scaling models in architecture ensures that all linear measurements maintain consistent proportional integrity. Manufacturing processes rely on linear scaling factors to produce scaled down prototype components. Map reading utilizes constant ratios to translate drawing dimensions into real world distances. Option A incorrectly doubles both numbers and uses a colon format resembling an unsimplified ratio. Option B represents the inverse squared relationship which applies to area rather than perimeter. Option C uses an incorrect numerical order and nonstandard ratio configuration.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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